Number Theory Discrete Logarithms in GF(p) the inverse problem to exponentiation is that of finding the discrete logarithm of a number modulo p find x where ax=b mod p while exponentiation is relatively easy, finding discrete logarithms is generally a hard problem, with no easy way in this problem, we can show that if p is prime, then there al ways exists an a such that there is al ways a discrete logarithm for any b!=0 successive powers ofa"generate"the group mod p such an a is called a primitive root and these are also relatively hard to findNumber Theory • Discrete Logarithms in GF(p) – the inverse problem to exponentiation is that of finding the discrete logarithm of a number modulo p – find x where ax = b mod p – while exponentiation is relatively easy, finding discrete logarithms is generally a hard problem, with no easy way – in this problem, we can show that if p is prime, then there always exists an a such that there is always a discrete logarithm for any b!=0 • successive powers of a "generate" the group mod p – such an a is called a primitive root and these are also relatively hard to find